Physicists Discover 'Impossible' Topological State in Quantum Material
TU Wien Findings Challenge Long-Standing views of Particle-Based Physics
Scientists at TU Wien have uncovered an unexpected state in a quantum material—one that was long thought to be impossible—prompting calls for a broader definition of topological states. The breakthrough has been reported in Nature Physics.
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Why Classical Particle Theory Still Shapes Modern Physics
Although quantum theory tells us that particles behave like waves, making their exact position uncertain, physicists often rely on classical intuition. In many cases, it remains remarkably effective to picture particles as tiny objects moving through space at a defined speed.
This classical picture underpins how researchers describe electrical current in metals, where electrons are imagined to race through the material, accelerating or bending under the influence of electromagnetic fields.
Even many of today's most advanced theories till rely on a particle-based view of electrons, including the concept of topological states—an achievement recognized with the 2016 Nobel Prize in Physics.
When the Particle Picture Breaks Down
Yet some materials exist where this picture collapses entirely. In such systems, electrons can no longer be described as tiny particles with a definite position or a single, well-defined velocity.
Researchers at TU Wien have now demonstrated that these unconventional materials can still display topological behaviour, despite the absence of particle-like motion. Their findings reveal that topological states are far more general than previously assumed, showing that two seemingly incompatible ideas can, in fact, coexist.
Quantum-Critical Behaviour in CeRu₄Sn₆
"The classical view of electrons as tiny particles that collide as they flow through a material is remarkably resilient," explains Prof. Silke Bühler-Paschen of TU Wien's Institute of Solid State Physics. "With suitable refinements, it even applies to complex materials where electrons interact strongly with one another."
Yet there conditions under which this picture breaks down entirely, with charge carriers losing their particle-like identity. This appears to be the case for the compound cerium-ruthenium-tin (CeRu₄Sn₆), recently studied at TU Wien under ultra-low temperature conditions.
"Close to absolute zero, the material shows a distinctive form of quantum-critical behaviour," says Diana Kirschbaum, lead author of the study. "It fluctuates between two competing states, as though unable to settle on either. In this regime, the quasiparticle concept is believed to no longer apply."
Topology Explained: Rolls, Apples and Doughnuts
Separate from the experimental breakthrough, the material was also examined theoretically, with researchers concluding that it should host topological states.
"Topology is a concept borrowed from mathematics, used to distinguish between different geometric structures," explains Silke Bühler-Paschen.
- An apple is topologically equivalent to a bread roll
- A doughnut is fundamentally different due to its hole, which cannot be created by smooth deformation.
In much the same way, states of matter can be classified: particle energies, velocities and even the alignment of spin with motion can obey strict geometric rules—an idea that makes topological properties exceptionally robust.
Minor disturbances, such as imperfections in a material, leave these properties unchanged. This robustness is why topological effects attract strong interest for:
- Quantum information storage
- Next-generation sensors
- Controlling electric currents without magnetic fields
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A Theoretical Contradiction Emerges
Despite its abstract nature, the topological description of particle behaviour has traditionally depended, at least indirectly, on a classical particle picture.
"These theories assume quantities like velocity and energy are well defined," explains Diana Krischbaum.
"In our material, however, such well-defined velocities and energies appear to be absent. It displays a form of quantum-critical behaviour that conflicts with a particle-based view."
Even so, simplified theoretical models that overlooked these non-particle features had already predicted that the material would exhibit topological properties—creating a clear contradiction.
Curiosity Leads to a Breakthrough
As a result, Silke Bühler-Paschen's team initially hesitated to pursue the theoretical prediction of topology. In the end, however, scientific curiosity prevailed.
At ultra-low temperatures—less than one degree above absolute zero —Diana Kirschbaum detected unmistakable experimental evidence of topology: a spontaneous, or anomalous, Hall effect.
Unlike the conventional Hall effect, which requires a magnetic field, this deflection emerged purely from topological effects, without any external magnetic influence.
Most strikingly, the charge carriers behaved as though they were particles, despite the apparent failure of the particle picture in this material.
"This was the crucial insight that allowed us to show, beyond any doubt, that the established view needs to be reconsidered," says Silke Bühler-Paschen.
Fluctuations Drive the Topological Effect
"And there is more," adds Diana Kirschbaum. "The topological effect reaches its peak precisely in the regime where the material shows the strongest fluctuations."
When these fluctuations are damped by pressure or magnetic fields, the topological behaviour disappears—revealing a direct link between quantum criticality and topology.
Topological States Are More General Than Thought
"This came as a huge surprise," says Silke Bühler-Paschen. "It shows that topological states need to be defined in far more general terms."
The researchers describe the newly identified phase as an emergent topological semimetal and collaborated closely with Rice University in Texas. There, Lei Chen, co-first author of the study, developed a new theoretical framework in the group of Prof. Qimiao Si, uniting quantum criticality with topology.
"In fact, topological properties do not require a particle-based picture at all," Bühler-Paschen explains. "The concept can be broadened, with topological distinctions emerging in a more abstract, mathematical sense. More remarkably still, our experiments indicate that topology can arise precisely because particle-like states are absent."
Why This Discovery Matters
The discovery points to a powerful new strategy for identifying topological materials.
"We now know that searching for topological behaviour in quantum-critical materials is not only worthwhile, but perhaps especially promising," Bühler-Paschen adds.
Because quantum-critical behaviour appears across many different classes of materials and can be identified reliably, this connection could lead to the discovery of an entirely new family of emergent topological materials.
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